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//======================================================================= // Copyright 1997, 1998, 1999, 2000 University of Notre Dame. // Copyright 2004 The Trustees of Indiana University // Authors: Andrew Lumsdaine, Lie-Quan Lee, Jeremy G. Siek // // Distributed under the Boost Software License, Version 1.0. (See // accompanying file LICENSE_1_0.txt or copy at // http://www.boost.org/LICENSE_1_0.txt) //======================================================================= #ifndef BOOST_GRAPH_SEQUENTIAL_VERTEX_COLORING_HPP #define BOOST_GRAPH_SEQUENTIAL_VERTEX_COLORING_HPP #include #include #include #include #include #ifdef BOOST_NO_TEMPLATED_ITERATOR_CONSTRUCTORS #include #endif /* This algorithm is to find coloring of a graph Algorithm: Let G = (V,E) be a graph with vertices (somehow) ordered v_1, v_2, ..., v_n. For k = 1, 2, ..., n the sequential algorithm assigns v_k to the smallest possible color. Reference: Thomas F. Coleman and Jorge J. More, Estimation of sparse Jacobian matrices and graph coloring problems. J. Numer. Anal. V20, P187-209, 1983 v_k is stored as o[k] here. The color of the vertex v will be stored in color[v]. i.e., vertex v belongs to coloring color[v] */ namespace boost { template < class VertexListGraph, class OrderPA, class ColorMap > typename property_traits< ColorMap >::value_type sequential_vertex_coloring( const VertexListGraph& G, OrderPA order, ColorMap color) { typedef graph_traits< VertexListGraph > GraphTraits; typedef typename GraphTraits::vertex_descriptor Vertex; typedef typename property_traits< ColorMap >::value_type size_type; size_type max_color = 0; const size_type V = num_vertices(G); // We need to keep track of which colors are used by // adjacent vertices. We do this by marking the colors // that are used. The mark array contains the mark // for each color. The length of mark is the // number of vertices since the maximum possible number of colors // is the number of vertices. std::vector< size_type > mark(V, std::numeric_limits< size_type >::max BOOST_PREVENT_MACRO_SUBSTITUTION()); // Initialize colors typename GraphTraits::vertex_iterator v, vend; for (boost::tie(v, vend) = vertices(G); v != vend; ++v) put(color, *v, V - 1); // Determine the color for every vertex one by one for (size_type i = 0; i < V; i++) { Vertex current = get(order, i); typename GraphTraits::adjacency_iterator v, vend; // Mark the colors of vertices adjacent to current. // i can be the value for marking since i increases successively for (boost::tie(v, vend) = adjacent_vertices(current, G); v != vend; ++v) mark[get(color, *v)] = i; // Next step is to assign the smallest un-marked color // to the current vertex. size_type j = 0; // Scan through all useable colors, find the smallest possible // color that is not used by neighbors. Note that if mark[j] // is equal to i, color j is used by one of the current vertex's // neighbors. while (j < max_color && mark[j] == i) ++j; if (j == max_color) // All colors are used up. Add one more color ++max_color; // At this point, j is the smallest possible color put(color, current, j); // Save the color of vertex current } return max_color; } template < class VertexListGraph, class ColorMap > typename property_traits< ColorMap >::value_type sequential_vertex_coloring( const VertexListGraph& G, ColorMap color) { typedef typename graph_traits< VertexListGraph >::vertex_descriptor vertex_descriptor; typedef typename graph_traits< VertexListGraph >::vertex_iterator vertex_iterator; std::pair< vertex_iterator, vertex_iterator > v = vertices(G); #ifndef BOOST_NO_TEMPLATED_ITERATOR_CONSTRUCTORS std::vector< vertex_descriptor > order(v.first, v.second); #else std::vector< vertex_descriptor > order; order.reserve(std::distance(v.first, v.second)); while (v.first != v.second) order.push_back(*v.first++); #endif return sequential_vertex_coloring(G, make_iterator_property_map(order.begin(), identity_property_map(), graph_traits< VertexListGraph >::null_vertex()), color); } } #endif